Joint extreme values of \(L\)-functions (Q2172510)

In the theory of zeta functions, one natural problem is to find extreme values of the zeta function on a given vertical line lying in the right half of the critical strip. More precisely, It is well known that if \(L\) is a function in the Selberg class satisfying the Selberg orthonormality conjecture (SOC) then on every vertical line \(s = \sigma + it\) with \(\sigma \in (1/2, 1)\), the \(L\)-function takes large values of size \(\exp (c (\log t)^{1-\sigma}/\log \log t)\) inside a small neighborhood. In the paper under review, the authors prove a similar result by showing the existence of closely spaced extreme values on a given vertical segment, for any collection of \(L\)-functions \(L_1, L_2,\dots, L_k\) in the Selberg class which have polynomial Euler product and satisfy he Selberg orthonormality conjecture.